Problem: Solve for $x$ and $y$ using elimination. ${-x+3y = 9}$ ${x+5y = 23}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-x$ and $x$ cancel out. $8y = 32$ $\dfrac{8y}{{8}} = \dfrac{32}{{8}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {-x+3y = 9}\thinspace$ to find $x$ ${-x + 3}{(4)}{= 9}$ $-x+12 = 9$ $-x+12{-12} = 9{-12}$ $-x = -3$ $\dfrac{-x}{{-1}} = \dfrac{-3}{{-1}}$ ${x = 3}$ You can also plug ${y = 4}$ into $\thinspace {x+5y = 23}\thinspace$ and get the same answer for $x$ : ${x + 5}{(4)}{= 23}$ ${x = 3}$